186 ANALYTICAL MECHANICS heat into work special means, such as heat engines, etc., have to be used/ which do not belong to the domain of 'ordinary mechanics; therefore work done against frictional forces is considered as lost. On the other hand work which Is done against gravitational forces or against kinetic reactions is directly available for mechanical work. 151. Energy. Potential, Kinetic, and Heat Energy.—Energy may be defined as work which is stored up. Work stored up in overcoming kinetic reactions is called kinetic energy. Work stored up while overcoming nonfrictional forces, such as gravitational forces, is called potential energy. Work done while overcoming frictional forces is called heat energy. 152. Transformation of Energy. — Potential, kinetic, and Jheat energy are different (at least apparently*) forms of the tsame physical entity, i.e., energy. Energy may be changed : from any one of these forms into any other form. Whenever ;such a change takes place energy is said to be transformed. 'Transformation of energy is always accompanied by work. In fact the process of doing work is that of transformation of energy. The amount of energy transformed equals the amount of work done. The units and dimensions of energy are the same as those ,of work. KINETIC ENERGY. '153. Kinetic Energy of a Particle. — By definition kinetic ^energy equals the work done against the kinetic reaction in giving the particle its velocity. Since there is no motion along the normal to the path of the particle no work is done against the normal component of the kinetic reaction. Therefore we need only consider the work done against the tangential component. * Recent developments in physical sciences tend to show that differences between different forms of energy are only apparent and that all forms of •• energy are, in the last analysis, kinetic.